MMC Capacitor Power Handling Calculations

Capacitor Energy per Bang

ECAP = 0.5 Co (VP / NLINE)2

Where:
ECAP = Energy Stored in Single Capacitor per Bang (Joules)
Co = Capacitance of a Single Capacitor (Farads)
VP = Gap Firing Voltage (Volts)
NLINE = Number of Capacitors per String

Internal Resistance of a Single Capacitor

RCAP = TANd / (2 p Co F)

Where:
RCAP = Internal Real Resistance of a Single Capacitor (Ohms)
TANd = Dissipation Factor
Co = Capacitance of a Single Capacitor (Farads)
F = Fundamental Frequency of Primary Circuit (Hz)

F (kHz)    TANd
10            0.0004
50            0.0008
100          0.0010
200          0.0016
300          0.0024
400          0.0040

Power Dissipation per Small Capacitor

Wo = KSYNC BPS ECAP RCAP / (RCAP + RPRI)

Where:
Wo = Power Dissipation per Small Capacitor (Watts)
KSYNC = 1 for Synchronous Gap or 0.5 for Non-Synchronous Gap
BPS = Bangs per Second
ECAP = Energy Stored in Single Capacitor per Bang (Joules)
RCAP = Internal Real Resistance of a Single Capacitor (Ohms)
RPRI = Primary Circuit Equivalent Resistance (~3 Ohms)

Temperature Rise of Small Capacitor

To = Wo Ko

Where:
To = Temperature Rise of Small Capacitor (° C)
Wo = Power Dissipation per Small Capacitor (Watts)
Ko = Small Capacitor Thermal Dissipation Factor (° C / Watt)

5                                    250
7.5                                 167
10                                  133
15                                  83
22.5                               67
27.5                               40
37.5                               33

Reliability

To (° C)     Reliability
0 - 5          Very Good
5 - 10        Good
10 -15       ?

Example:

Total Primary Capacitance = 28nF
Fundamental Frequency = 100 kHz
Firing Voltage = 21000 Volts (15000 VAC)
BPS = 120
Gap = Non-Synchronous
Primary Capacitor = 7 strings of 14 x 56nF small caps whose lead spacing is 27.5 mm and the AC voltage rating is 630 VAC.

How reliable would this be?

ECAP = 0.5 Co (VP / NLINE)2
ECAP = (0.5) (56 x 10-9) (21000 / 14)2
ECAP = 0.063 Joule

RCAP = TANd / (2 p Co F)
RCAP = 0.0010 / (2 p (56 x 10-9) 100000)
RCAP = 0.02842 Ohm

Wo = KSYNC BPS ECAP RCAP / (RCAP + RPRI)
Wo = (0.5) (120) (0.063) (0.02842) / (0.02842 + 3)
Wo = 0.0355 Watt

To = Ko Wo
To = 40 x 0.0355
To = 1.42 ° C

The reliability should be "Very Good".